This document summarizes a study that used Reed-Solomon codes with a downlink Long Term Evolution (LTE) system over an LTE Multiple-Input Multiple-Output (MIMO) channel to improve performance. Reed-Solomon codes were chosen because they have low decoding complexity compared to convolutional and turbo codes. Simulation results showed that using Reed-Solomon codes decreased the bit error rate more than convolutional or turbo codes. Additionally, increasing the number of antennas in the LTE-MIMO channel provided further improvements to downlink LTE system performance. BPSK modulation provided better performance gains compared to QPSK when used with Reed-Solomon codes over the LTE-MIMO channel.

1. TELKOMNIKA, Vol.16, No.6, December 2018, pp.2563~2569
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v16i6.9177  2563
Received March 4, 2018; Revised September 14, 2018; Accepted October 8, 2018
RS Codes for Downlink LTE System over
LTE-MIMO Channel
Ghasan Ali Hussain*, Lukman Audah
Wireless and Radio Science Centre (WARAS), Faculty of Electrical and Electronic Engineering,
Universiti Tun Hussein Onn Malaysia, Parit Raja, 86400 Batu Pahat, Johor, Malaysia
*Corresponding author, e-mail: ghasan.alabaichy@uokufa.edu.iq
Abstract
Nowdays, different applications require a modern generation of mobile communication systems;
long term evolution (LTE) is a candidate to achieve this purpose. One important challenge in wireless
communications, including LTE systems, is the suitable techniques of controlling errors that degrade
system performance in transmission systems over multipath fading channels. Different forward Error
correction (FEC) techniqes are required to improve the robustness of transmission channels. In this paper,
Reed-Solomon (RS) codes were used with a downlink LTE system over a LTE-MIMO channel. This
research contributes by combining RS codes that have low decoding complexity (by using hard decision
decoding) with a LTE-MIMO channel to improve downlink LTE system performance. The results show that
using RS codes clearly improves LTE system performance and thus decreases Bit Error Rates (BER)
more than convolutional and turbo codes which have high decoding complexity. Lastly, the results show
also extra improvements of downlink LTE system performance by increasing the number of antennas of
the LTE-MIMO channel.
Keywords: LTE, RS, MIMO, BPSK, QPSK
Copyright © 2018 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
Using data and voice services in mobile communication systems has become a life
necessary today, so there is huge demand for improvements in these technologies. LTE is a
good solution to provide these applications and thus is a candidate for future technological
innovation [1, 2] due to it supports high data rates systems [3, 4]. Orthogonal Frequency
Division Multiplexing (OFDM) is considered a key technology of 3GPP LTE and 4G, as well as
802.11n WLAN and IEEE 802.16m WiMAX, due to its combating selective fading channel. It can
be easily implemented using Discrete Fourier Transform (DFT), which makes OFDM an
attractive technology for Broadband mobile wireless. Combining the Multi Input Multi Output
(MIMO) technique with OFDM provides a good solution for 4G networks [5]. MIMO technique is
applied through using multi antennas in both of transmitter and receiver to improve data rates,
channel capacity, network coverage and link reliability [6].
The channel in mobile environments is divided into frequency and time selective fading;
using OFDM will combat any Inter Symbol Interference (ISI) that occurs [5]. An orthogonal
Frequency Division Multiplexing Access (OFDMA) is used in the transmission scheme for
downlink LTE; this is a multi-user version of OFDM [7, 8]. When time-invariance exists in
the frequency selective channel, OFDM systems support using simple one-tap equalization [9].
In contrast, in high mobility cases, performance is degraded and equalization is needed to
improve performance [10, 11]. Achieving robustness in the radio link of any wireless
communication systems requires channel coding techniques. When performing source coding,
channel coding will add a new controlled redundancy [12].
Powerful techniques are needed in a LTE system to control errors in the transmission
channel. Adding parity bits to the signal data stream is considered a method of error control;
the goal of adding these bits is to detect and correct errors [12, 13]. Some powerful techniques
for FEC have been suggested in LTE system such as convolutional codes in [13-15], although
their techniques improved the system performance but they also faced the problem of high
convolutional decoding complexity [16]. In contrast, other studies such as [17-19] are adopted
turbo codes with LTE to improve the reliability. However, high decoding complexity is still a

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common demerit of turbo codes [20], as well the results of the decoding are not stabile and thus
it is necessary to achieve the balance between the decoding performance and complexity [12].
In wireless communication systems, RS codes are widely used due to the high capability of
correcting burst errors and random errors. There are two RS decoding process; Soft Decision
Decoding (ASD) and Hard Decision Decoding (HDD). Practically, HDD is popular used in
different application due to its lower complexity than ASD [21]. Therefore, to achieve robust
error control in Downlink LTE system over LTE MIMO channel, RS codes (that using HDD)
which have low decoding complexity are proposed in this paper, while the channel capacity can
be enhanced using MIMO technique [6]. The performance of proposed system was tested using
a multipath fading LTE MIMO channel. The simulation was done using two types of modulation
(BPSK and QPSK) to show which type gives extra imporvement to the system performance.
2. The Proposed Method
The proposed Downlink LTE system by using RS codes has been depicted in Figure 1
to explain the whole block diagram of the proposed LTE system. While, the parameters of LTE
environments that used in the suggested LTE system design are explained in Table 1. In this
paper, MATLAB software has been used to evaluate the performance of LTE system over
LTE-MIMO channel in presence of multipath fading channel.
Figure 1. Proposed LTE system
Table 1. Simulation Environment of the LTE System
Transmission Bandwidth 20MHz
Channel
LTE-MIMO Channel
Multipath Fading Channel
Number of IFFT/FFT Points 2048
No. of Occupied Sub-carrier 1200
Cyclic Prefix Length 144
Modulation BPSK and QPSK
Sampling Rate 30.72MHz
Error Correcting Techniques Reed-Solomon Codes (HDD)
2.1. Reed-Solomon Codes
Reed and Solomon proposed a new type of ECC in [22] and called reed-solomon
codes. It is considered non-binary cyclic codes. The symbols of RS codes consist of positive
integer values (< 2) of m bit sequences. The form of RS codes is represented as [23].
RS(n, k) 0<k<n<2m+2
Since, n defined as total number of code symbols (in the encoded block) and the value
of data symbols k that have been encoded. Classic RS (n, k) code is as follows [23].

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(n, k)=(2m–1, 2m–1–2t)
The capability of the code’s symbol error correcting is represented by t, where (t=n-k)
represents the parity symbols number. RS codes are also considered cyclic and linear codes.
RS codes have a good capability of error correction, especially when dealing with burst of
errors [23].
In general, RS decoding procedure phases as following [24]:
a. Determine the syndrome from received codeword.
b. From syndrome and using own derived equations could select the error location and error
value polynomial.
c. By using error value polynomial and error location, could correct the symbols that have
errors.
Suppose, α is the primitive element of GF (q) and αq-1 equal to 1. Then, RS code can be
obtained by the following polynomial [25].
g(x) = (X-α) (X-α2) …..(X-αn-k)
= (X-α) (X-α2) …(X-α2t)
= g0+g1 X+g2 X2+ . . . . .+ g2t-1 X2t-1+ g2t X2t (1)
By a given generator polynomial of (1), an RS code CRS(n , n-2t) is a linear and cyclic
block generated consist of code polynomial c(x) that have (n-1) degree or less. All coefficients of
these polynomials are elements in GF(2m). When multiplies the code polynomials by generator
polynomial, will obtaining all its roots [25].
Assume m(X) is message polynomial and created as in (2). While, all coefficients of
these message polynomials are also elements of GF(2m). The systematic method is used to
obtain the remainder p(x) through divided Xn-k m(X) by g(X) as in (3) [25].
m(X) = m0+ m1X+m2X2+…….+mk-1 Xk-1 … … … …(2)
Xn-k m(X) = q(X)g(X) + p(X) (3)
Table 2. The Galois Field GF(23) Produced by pi (X)=1+X+X3
Expression Repr. Polynomial Repr. Vector Repr.
0 0 0 0 0
1 1 1 0 0
𝛼 𝛼 0 1 0
𝛼2
𝛼2 0 0 1
𝛼3
1+𝛼 1 1 0
𝛼4
𝛼+𝛼2
0 1 1
𝛼5
1+ 𝛼+𝛼2 1 1 1
𝛼6
1+𝛼2
1 0 1
2.2. Interleaver/ De-Interleaver
To combat the burst of errors in the transmission channel, an interleaver has been used
to re-request input bit series to a non-adjacent method [26]. Where, using the interleaving
process after RS encoder is very important to enhancing the capability of error correcting in the
receiver [27]. Therefore, by using Interleaver/De-Interleaver process in LTE system, the system
will be more effictive in combating the errors and thus improving the system performance
through decreasing BER.
2.3. Modulation
Two modulation schemes have been used in this paper for comparison in the proposed
system. We chose both BPSK and QPSK, due to their good performance compared with other
types of modulation. Where, lower order modulations (for instance QPSK and BPSK) improve
system performance better than high order modulations (for instance as 64-QAM and 16-QAM)
in terms of BER and Signal to Noise Ration (SNR) [28].

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2.4. LTE MIMO Channel
A 3GPP-LTE of Release 10 was created in this channel; it was particular for the MIMO
system over multipath fading channel. The signal has been passed via multipath fading channel
using the LTE-MIMO channel [29]. First, a MIMO system using two transmitter and receiver
antennas was used, then four transmitter and receiver antennas were used in a second
scenario.
3. Results and Discussion
MATLAB software was used in this paper to simulate a Downlink LTE system. It was
done to test the proposed system performance over a multipath fading channel using a
LTE-MIMO channel. The performance of Downlink LTE system was improved using RS coding
technique for both of modulation types BPSK and QPSK. The system performance is presented
by the curve of BER versus SNR.
The comparison of the system performance was done among each of un-coded,
convolutional codes, turbo code and reed Solomon codes to show the improvements of BER for
each case. Figure 2 shows the simulation results of RS-Downlink LTE system performance
using BPSK over (2X2) LTE-MIMO channel against each of un-coded, convolutional codes,
turbo code. It is clearly shows that the performance of un-coded system was the worst, while
the performance began to improve after (8 dB) SNR using convolutional and turbo codes.
The performance when using RS codes was the best compared with un-coded, convolutional
and turbo codes for all values of SNR. Therefore, using RS codes with Downlink LTE system
over (2X2) LTE-MIMO channel gave good coding gains and thus clearly improved system
performance more than using both of convolutional and turbo codes with BPSK.
Figure 2. The Downlink LTE system performance over LTE-MIMO channel (BPSK)
Figure 3 shows the simulation results of RS- Downlink LTE system performance using
QPSK over LTE-MIMO channel against each of un-coded, convolutional code, turbo code.
The performance of the uncoded system was also the worst with a QPSK modulation scheme
compared with using coding techniques. Then, the system performance improved starting after
around 12dB by using both of convolutional and turbo codes. The best performance for each
values of SNR compared with all of uncoded, convolutional and turbo codes was when using
RS codes. Therefore, the Downlink LTE system performance over (2X2) LTE-MIMO channel

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clearly improved for both BPSK and QPSK modulation schemes compared with using both of
convolutional or turbo codes, as shown in both of Figures 2 and 3.
Figure 3. The Downlink LTE system performance over LTE-MIMO channel (QPSK)
Figure 4 shows a comparison of proposed system performance when using BPSK
versus QPSK modulation schemes. The Downlink LTE system performance over (2X2)
LTE-MIMO channel clearly improved more with BPSK than with QPSK modulation scheme for
both uncoded and RS codes as shown in Figure 4. The coding gain achieved using RS codes
with BPSK in the proposed system was around 4 dB at 10-2 compared with QPSK.
Figure 4. Comparison between Downlink LTE system performance over LTE-MIMO channel
(QPSK versus BPSK)

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Figure 5 shows the comparison between using (2X2) versus (4X4) MIMO channel for
the proposed system. The comparison shows extra improvement using a (4X4) compared with
using a (2X2) antennas MIMO system. Therefore, the Downlink LTE system performance was
enhanced by increasing the number of antennas in the MIMO channel for both of BPSK and
QPSK modulation schemes.
Figure 5. Downlink LTE system performance over LTE-MIMO channel
4. Conclusion
One of the important challenges facing wireless communication systems, including LTE,
is controlling errors in transmission systems over multipath fading channels. The simulation of a
Downlink LTE system performance over LTE-MIMO channel was carried out using Reed-
Solomon (RS) codes. The combining of RS codes with a LTE-MIMO channel to improve
the downlink LTE system performance is a novel contribution of this paper. A comparison
between using RS codes and both of convolutional and turbo codes that already suggested in
Downlink LTE system was presented in this paper. The results show an advantage of using RS
codes compared with all of uncoded, convolutional and turbo codes in the proposed system’s
performance. On the other hand, the coding gain achieved in the proposed system using RS
codes with BPSK was around 4 dB at 10-2 compared with QPSK. This research proves that
Downlink LTE system performance is improving when utilizing RS codes and extra
improvements can be gained by increase the number of antennas in the LTE-MIMO channel for
both the BPSK and QPSK modulation schemes.
Acknowledgment
This research is funded by the Ministry of Higher Education Malaysia under
Fundamental Research Grant Scheme Vot No. 1627 and partially sponsored by Universiti Tun
Hussein Onn Malaysia.
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